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Low-shear three-dimensional equilibria and vacuum magnetic fields with flux surfaces

Part of: Focus on Fusion

Published online by Cambridge University Press:  02 April 2019

Wrick Sengupta Open the ORCID record for Wrick Sengupta [Opens in a new window]  and
Harold Weitzner
Wrick Sengupta*
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
Harold Weitzner
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
*
†Email address for correspondence: wricksg@gmail.com
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Abstract

Stellarators are generically small current and low plasma beta devices. Often the construction of vacuum magnetic fields with good magnetic surfaces is the starting point for an equilibrium calculation. Although in cases with some continuous spatial symmetry, flux functions can always be found for vacuum magnetic fields, an analogous function does not, in general, exist in three dimensions. This work examines several simple equilibria and vacuum magnetic field problems with the intent of demonstrating the possibilities and limitations in the construction of such states. Starting with a simple vacuum magnetic field with closed field lines in a topological torus (toroidal shell with a flat metric), we obtain a self-consistent formal perturbation series using the amplitude of the non-symmetric vacuum fields as a small parameter. We show that systems possessing stellarator symmetry allow the construction order by order. We further indicate the significance of stellarator symmetry in the amplitude expansion of the full ideal magnetohydrodynamics (MHD) problem as well. We then investigate the conditions that guarantee neighbouring flux surfaces given the data on one surface, by expanding in the distance from that surface. We show that it is much more difficult to find low shear vacuum fields with surfaces than force-free fields or ideal MHD equilibrium. Finally, we demonstrate the existence of a class of vacuum magnetic fields, analogous to ‘snakes’ observed in tokamaks, which can be expanded to all orders.

Keywords

plasma confinementplasma devicesplasma dynamics
Type
Research Article
Information
Journal of Plasma Physics , Volume 85 , Issue 2 , April 2019 , 905850209
Copyright
© Cambridge University Press 2019 

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